Spin-orbit coupled honeycomb magnets with the Kitaev interaction have received a lot of attention due to their potential of hosting exotic quantum states including quantum spin liquids. Thus far, the most studied Kitaev systems are 4d/5d-based honeycomb magnets. Recent theoretical studies predicted that 3d-based honeycomb magnets, including Na₂Co₂TeO₆ (NCTO), could also be a potential Kitaev system. Here, we have used a combination of heat capacity, magnetization, electron spin resonance measurements alongside inelastic neutron scattering (INS) to study NCTO’s quantum magnetism, and we have found a field-induced spin disordered state in an applied magnetic field range of 7.5 T < B (⊥ b-axis) < 10.5 T. The INS spectra were also simulated to tentatively extract the exchange interactions. As a 3d-magnet with a field-induced disordered state on an effective spin-1/2 honeycomb lattice, NCTO expands the Kitaev model to 3d compounds, promoting further interests on the spin-orbital effect in quantum magnets.

Magnetic frustrated materials are of great interest for their novel spin-dependent transport properties. We report an anisotropic anomalous Hall effect in the triangular itinerant ferromagnet ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. When the current flows along the $ab$ plane, ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ exhibits the conventional anomalous Hall effect below the Curie temperature $T_c$, which can be depicted by Karplus–Luttinger theory. On the other hand, the topological Hall effect shows up below $T_c$ with current along the $c$ axis. The enhancement of Hall resistivity can be attributed to the chiral effect during the spin-flop process.

In ordinary materials, electrons conduct both electricity and heat, where their charge-entropy relations observe the Mott formula and the Wiedemann-Franz law. In topological quantum materials, the transverse motion of relativistic electrons can be strongly affected by the quantum field arising around the topological fermions, where a simple model description of their charge-entropy relations remains elusive. Here we report the topological charge-entropy scaling in the kagome Chern magnet TbMn₆Sn₆, featuring pristine Mn kagome lattices with strong out-of-plane magnetization. Through both electric and thermoelectric transports, we observe quantum oscillations with a nontrivial Berry phase, a large Fermi velocity and two-dimensionality, supporting the existence of Dirac fermions in the magnetic kagome lattice. This quantum magnet further exhibits large anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects, all of which persist to above room temperature. Remarkably, we show that the charge-entropy scaling relations of these anomalous transverse transports can be ubiquitously described by the Berry curvature field effects in a Chern-gapped Dirac model. Our work points to a model kagome Chern magnet for the proof-of-principle elaboration of the topological charge-entropy scaling.

The semiconducting ferromagnet CrSiTe₃ is a promising candidate for two-dimensional magnet simply by exfoliating down to single layers. To understand the magnetic behavior in thin-film samples and the possible applications, it is necessary to establish the nature of the magnetism in the bulk. In this work, the critical behavior at the paramagnetic to ferromagnetic phase transition in single-crystalline CrSiTe₃ is investigated by bulk magnetization measurements. We have obtained the critical exponents (β = 0.170 ± 0.008, γ = 1.532 ± 0.001, and δ = 9.917 ± 0.008) and the critical temperature T_C = 31.0 K using various techniques such as modified Arrott plot, Kouvel-Fisher plot, and critical isotherm analysis. Our analysis suggests that the determined exponents match well with those calculated from the results of renormalization group approach for a two-dimensional Ising model coupled with long-range interaction.

Fe₃GeTe₂ is a promising candidate for van der Waals bonded ferromagnet because of its high Curie temperature and the prediction that its ferromagnetism can maintain upon exfoliating down to single layer. Here, we have reported the critical behavior to understand its ferromagnetic exchange. Based on various techniques including modified Arrott plot, Kouvel-Fisher plot, and critical isotherm analysis, a set of reliable critical exponents (β = 0.327 ± 0.003, γ = 1.079 ± 0.005, and δ = 4.261 ± 0.009) has been obtained. The critical behavior suggests a three-dimensional long-range magnetic coupling with the exchange distance decaying as J(r) ≈ r^−4.6 in Fe₃GeTe₂. The possible origin of three-dimensional magnetic characteristics in van der Waals bonded magnets is discussed.

Kagome magnet has been found to be a fertile ground for the search of exotic quantum states in condensed matter. Arising from the unusual geometry, the quantum interactions in the kagome lattice give rise to various quantum states, including the Chern-gapped Dirac fermion, Weyl fermion, flat band and van Hove singularity. Here we review recent advances in the study of the R166 kagome magnet (RT₆E₆, R = rare earths; T = transition metals; and E = Sn, Ge, etc) whose crystal structure highlights the transition-metal-based kagome lattice and rare-earth sublattice. Compared with other kagome magnets, the R166 family owns the particularly strong interplays between the d electrons on the kagome site and the localized f electrons on the rare-earth site. In the form of spin-orbital coupling, exchange interaction and many-body effect, the quantum interactions play an essential role in the Berry curvature in both the reciprocal and real spaces of R166 family. We discuss the spectroscopic and transport visualization of the topological electrons hosted in the Mn kagome layer of RMn₆Sn₆ and the various topological effects due to the quantum interactions, including the Chern-gap opening, the exchange-biased effect, the topological Hall effect and the emergent inductance. We hope this work serves as a guide for future explorations of quantum magnets.